Minimal covering unrestricted location of obnoxious facilities: bi-objective formulation and a case study
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Minimal covering unrestricted location of obnoxious facilities: bi‑objective formulation and a case study Kayhan Alamatsaz1 · S. M. T. Fatemi Ghomi1 · Mehdi Iranpoor2 Accepted: 22 October 2020 © Operational Research Society of India 2020
Abstract This paper addresses the problem of locating obnoxious facilities aiming to mitigate the adverse effects of such facilities by minimizing the total covered demand and reducing the harmful effects of multiple-coverage by placing the facilities far from each other. Unlike the classical approaches, it is assumed that the facilities can be located not only on the nodes but also on the network’s edges. Additionally, demands are not restricted to reside on the nodes but are distributed along the edges. In such a condition, the problem of locating obnoxious facilities is much closer to the real-world. A bi-objective mixed-integer linear programming formulation is developed for this novel problem. This bi-objective problem is solved using the ε-constraint method and NSGA-II. The ε-constraint method can be used to solve the small and medium-sized problems optimally in a reasonable time. As a realistic example, this approach is implemented in a case study in Isfahan for a particular urban planning problem. The case is locating obnoxious solid waste disposal facilities that should be located as far away as possible and simultaneously cover the least demands. Large scale problems cannot be solved efficiently using the ε-constraint method. However, the numerical analysis showed the efficiency and effectiveness of the NSGA-II approach for these problems. Finally, sensitivity analysis is applied to evaluate the effect of changes in coverage distance and the number of facilities on the conflicting objective functions. Keywords Obnoxious facility · Minimal covering · p-Dispersion · Bi-objective optimization · NSGA-II · Case study * Mehdi Iranpoor [email protected] Kayhan Alamatsaz [email protected] S. M. T. Fatemi Ghomi [email protected] 1
Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran
2
Department of Industrial and Systems Engineering, Isfahan University of Technology, 84156‑83111 Isfahan, Iran
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1 Introduction The maximal covering location problem (MCLP) deals with locating desirable facilities with the aim of maximizing the total covered demand [2]. On the contrary, the minimal covering location problem (MinCLP) deals with placing obnoxious (i.e., undesirable) facilities in order to minimize the covered demand [10]. Some instances of undesired facilities are solid waste disposal sites, nuclear reactors, airports [25], industrial plants [36], recycling centers [5], and sewage farms which usually have harmful effects on people who live nearby and adverse impacts on the environment. On the other hand, the p-dispersion problem tries to locate the facilities as far away as possible from each other. This problem is suitable for locating facilities exposed to the risk of attacks such as military insta
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